Autoregressive moving average modeling for feedforward and feedback Tomlinson-Harashima precoder filters

ABSTRACT

Apparatus and methods provide a Tomlinson-Harashima precoder scheme in which a feedback filter may be constructed to match an approximated feedforward filter, where the feedforward filter is approximated using autoregressive moving average modeling.

RELATED APPLICATION

This application is a U.S. National Stage Filing under 35 U.S.C. 371from International Patent Application Serial No. PCT/RU2005/000683,filed Dec. 29, 2005, and published on Jul. 5, 2007 as WO 2007/075107 A1,which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

Embodiments of the invention relate generally to precoders forcommunication channels.

BACKGROUND

Channels in a communication network may typically experience channeldistortion: This channel distortion may result in intersymbolinterference (ISI), which essentially is the spreading of a signal pulseoutside its allocated time interval, causing interference with adjacentpulses. If a communication channel is uncompensated with respect to itsintersymbol interference, high error rates may result. Various methodsand designs are used for compensating or reducing intersymbolinterference in a signal received from a communication channel. Thecompensators for such intersymbol interference are known as equalizers.Various equalization methods include use of maximum-likelihood (ML)sequence detection, linear filters with adjustable coefficients,decision-feedback equalization (DFE), and Tomlinson-Harashima precodersfor ISI cancellation. To provide higher-speed reliable datacommunication, what is needed are enhanced schemes for providing channelequalization, which at the same time can be implemented without asignificant amount of complexity.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a flow diagram of features of an embodiment of amethod to provide a Tomlinson-Harashima precoder scheme having afeedback filter matched to a feedforward filter with the feedforwardfilter approximated using autoregressive moving average modeling.

FIG. 2 depicts a network that includes an embodiment of a precoderconfigured according to a Tomlinson-Harashima precoder scheme having afeedback filter matched to a feedforward filter with the feedforwardfilter approximated using autoregressive moving average modeling.

FIG. 3 shows a simulation of an embodiment of a feedback filter in aTomlinson-Harashima precoder scheme using autoregressive moving averagemodeling as compared to a feedback filter of a standardTomlinson-Harashima precoder.

FIG. 4 shows a simulation of an embodiment of a feedforward filter in aTomlinson-Harashima precoder scheme using autoregressive moving averagemodeling as compared to a feedforward filter of a standardTomlinson-Harashima precoder.

FIG. 5 shows a simulation of an embodiment of a Tomlinson-Harashimaprecoder scheme using autoregressive moving average modeling withrespect to a bit error rate for a 100 m category 7 cable.

FIG. 6 illustrates a block diagram of an embodiment of a system havingan embodiment of a Tomlinson-Harashima precoder scheme based onautoregressive moving average modeling.

DETAILED DESCRIPTION

The following detailed description refers to the accompanying drawingsthat show, by way of illustration, specific details and embodiments inwhich the invention may be practiced. These embodiments are described insufficient detail to enable those skilled in the art to practice thepresent invention. Other embodiments may be utilized and structural,logical, and electrical changes may be made without departing from thescope of the invention. The various embodiments disclosed herein are notnecessarily mutually exclusive, as some disclosed embodiments can becombined with one or more other disclosed embodiments to form newembodiments. The following detailed description is, therefore, not to betaken in a limiting sense.

FIG. 1 illustrates a flow diagram of features of an embodiment of amethod to provide a Tomlinson-Harashima precoder scheme having afeedback filter matched to a feedforward filter with the feedforwardfilter approximated using autoregressive moving average modeling. At110, a feedforward filter may be approximated using autoregressivemoving average modeling. Autoregressive moving average (ARMA) modelingis a mathematical modeling of a time series based on the assumption thateach value of the series depends only on a weighted sum of the previousvalues of the same series (autoregressive component) and on a weightedsum of the present and previous values of a different time series(moving average component) with the addition of a noise factor. Forexample, if y(k) is the k-th value of a time series to model, u(k) is adifferent time series, and n(k) is noise, then an ARMA model (b,a) oforder (N,M) may be represented by:

$y_{k} = {{\sum\limits_{i = 1}^{N}{a_{i}y_{k - i}}} + {\sum\limits_{i = 0}^{M}{b_{i}u_{k - i}}} + n_{k}}$

In an embodiment, an approximated feedforward filter may be realized ina Tomlinson-Harashima precoder scheme. In such a scheme, a feedforwardfilter is located at a receiver end of a communication channel and afeedback filter is located at a transmit end of a communication channel.Various approaches to determining coefficients for a filter such as afeedforward filter include using the well-known Levinson-Durbinalgorithm. In an embodiment, the Steiglitz-McBride method may be appliedto finding infinite impulse response (IIR) filter coefficients to buildan IIR filter with the number of poles not equal to the number of zeros,as opposed to the Levinson-Durbin algorithm.

The Steiglitz-McBride method is a fast iterative algorithm that solvesfor the numerator and denominator coefficients of a rational transferfunction simultaneously in an attempt to minimize the signal errorbetween an output of a emit and the time-domain impulse response of theunit. In an embodiment, the Steiglitz-McBride algorithm may be used toapproximate a given time-domain response by an appropriate ARMA model ordigital rational transfer function. An ARMA model may be used togenerate a digital rational transfer function for a feedforward filterthat is used for an approximation of a given time-domain impulseresponse of the feedforward filter. The impulse response of the ARMAmodel may be expressed as b(z)/a(z). The Steiglitz-McBride algorithm maybe applied to solve for the numerator b(z) and the denominator a(z) suchthat the squared error is minimized between the impulse response ofb(z)/a(z) and the given time-time domain impulse response. Two variantsof the time-domain impulse response may be used as the given time-domainimpulse response. First, the impulse response of the feedforward filtermay be used and thereafter the impulse response of a target feedbackfilter may be used. The target feedback filter may be correlated to theapproximated feedforward filter. This algorithm usually convergesrapidly, but might not converge if the model order is too large.

At 120, a feedback filter to match the approximated feedforward filtermay be constricted. A target feedback filter defined by the polynomialB(z) may be constructed to match the result of the feedforward filterapproximation by generating the relationship B(z)=1−R(z)*H(z), where theoperator * is the convolution operator. The polynomial R(z) provides anARMA approximation of a feedforward filter for a channel having impulseresponse H(z). Then, the target feedback filter defined by thepolynomial B(z), where B(z)=1−R(z)*H(z), comprises, in a general way, anDIR filter. B(z) is a digital rational transfer function with its ownnumerator and denominator. The denominator of B(z) may be identical withthe denominator of R(z), where the denominator has a small size degree.In an embodiment, a denominator for B(z) has a degree of 3. Thenumerator of B(z) may have a large degree, typically of the order of 100or more. In an embodiment, a target feedback filter, which is defined bythe polynomial B(z), may be ARMA approximated to generate an IIR filtersolution having fewer filter taps. H(z) may be known at the transmit endand at the receive end. In an embodiment, a feedback filter may beconstructed by generating a target feedback filter from an approximationof a feedforward filter and by conducting autoregressive moving averagemodeling of the target feedback filter to form the feedback filter.

In various embodiments, ARMA modeling for feedforward and feedbackTomlinson-Harashima precoder filters provides for feedforward andfeedback filters that have relatively small size. Feedback andfeedforward filters in a classical Tomlinson-Harashima precoder (THP)are typically chosen to minimize mean square error (MSE) at the precoderoutput given some channel impulse response, which may result in THPhaving a large feedback filter for Ethernet 10 gigabit (10 G) cableshaving lengths ranging from about 100 meters to about 150 meters.

In an embodiment, a feedback filter in a Tomlinson-Harashima precoderscheme may be constructed to match a provided feedforward filter, wherethe feedforward filter is constructed using autoregressive movingaverage modeling. A set of feedforward filters may be approximated usingautoregressive moving average modeling corresponding to communicationchannels of varying characteristics, such as different channel lengths.The characteristics that define a feedforward filter in the set offeedforward filters may be provided to construct a feedback filter. Inan embodiment, a training mode process may be performed for acommunication arrangement using a Tomlinson-Harashima precoder schemesuch that once a feedforward filter is approximated using autoregressivemoving average modeling at a receive end of a communication channel, thecharacteristics of the feedforward filter may be provided to thetransmit end of the communication channel to construct a matchingfeedback filter.

FIG. 2 illustrates a network 200 that includes an embodiment of aprecoder 205 configured according to a Tomlinson-Harashima precoderscheme having a feedback filter 220 matched to a feedforward filter 260with feedforward filter 260 approximated using autoregressive movingaverage modeling. Feedforward filter 260 may be defined by polynomialR(z), where R(z) may be determined using autoregressive moving averagemodeling. Feedback filter 220 may be defined by target polynomial B(z)that may be matched to R(z). In an embodiment, target polynomial B(z)may be related to an ARMA approximation filter R(z) by B(z)=1−R(z)*H(z).In an embodiment, a feedback filter and a feedforward filter may be ARMAapproximated. A Tomlinson-Harashima precoding scheme provides forimplementation of a feedback filter at the transmitter end of thecommunication channel with a mechanism to limit output signal amplitude.Signal samples transmitted in channel 210 between node 202 and node 203are subjected to a feedback filter 220 and a modulo reduction functionM(x) 230 to avoid overflowing the signal bounds. Modulo reductionfunction 230 is a modulo operation to limit the amplitude of the signalsto be transmitted into channel 210. The feedback loop is closed withfeedback filter 220 coupled back to a summer 240 that receives thesignal samples. At the receive end of the communication channel, afeedforward filter 260 receives the transmitted symbols and provides afiltered signal to a receive modulo reduction function 250 that maps thesignal to symbol estimates in an operation effectively inverse tomap-reduction function 230. For a given THP scheme, two filter units areassociated with the precoder, feedback filter 220 at a transmit end of achannel and a feedforward filter 260 at a reception end of a channel. Inan embodiment, network 200 may be a 10 Gigabit Ethernet network in whichequalization is provided using an embodiment of a THP scheme.

A Tomlinson-Harashima precoder is to be the part of an Institute ofElectrical and Electronics Engineers (IEEE) standard, IEEE 802.3anstandard. In a draft, Draft P802.3an/D2.1, of IEEE standard Ethernet802.3an for 10GBASE-T having a formal expiration date of 21 Jul. 2005,use of a fixed set of Tomlinson-Harashima precoders for channelequalization during transmission over cables of different lengths wasindicated. The number of precoders in the precoder set is not defined,but the range is approximately from 4 to 8 fixed precoders. In contrastto measuring the channel impulse response and optionally tuning precoderfilters for this response before transmission, there will be a set ofTHP filters coefficients for all transmission conditions. This meansthat, during initialization, network cards for 10GBASE-T may estimatethe channel, but the precoders may not be constructed using the channelestimate. The precoders will be selected as one of the predefined set ofthe precoders. For a traditional THP, feedforward and feedback precoderfilters are chosen to minimize MSE at the precoder output given somechannel impulse response H(z), where M(x) denotes the modulo operator,which for the case of pulse amplitude modulation with M possible symbolvalues (M-PAM) with minimum signal distance d is given by

${M(x)} = {x - {{Md}\lfloor \frac{x + \frac{Md}{2}}{Md} \rfloor}}$A typical length for Ethernet 10G cables of acceptable ISI values isfrom about 100 m to about 150 m, but the length depends on cable type.For such a case, the THP feedback filter generally has a large size,where the filter size is defined by the number of filter taps. As thenumber of filter taps increases, the complexity for the implementationof the usual Tomlinson-Harashima precoder in 10G framework increases.

In an embodiment, a Tomlinson-Harashima precoding scheme includes afeedforward filter having ARMA approximated filter taps with a feedbackfilter constructed based on the feedforward filter and the channelimpulse response. The feedforward filter may have a small size. In anembodiment, a feedforward filter has 20 or fewer ARMA approximatedfilter taps. In an embodiment, a feedback filter matched to a small sizefeedforward may have a small size. In an embodiment, a feedback filtermay be ARMA approximated based on an ARMA approximated feedforwardfilter. In an embodiment, a feedback filter has 10 or fewer filter taps.In an embodiment, feedforward filter 260 and feedback filter 220 may beinfinite impulse response filters. In an embodiment, both feedbackfilter 220 and feedforward filter 260 may be specified as finite impulseresponse (FIR) filters. In an embodiment, one of feedback filter 220 andfeedforward filter 260 may be an IIR filter with the other filter beinga FIR filter. IIR filters typically meet a given set of specificationswith a much lower filter order than does a corresponding FIR filter. Inan embodiment, parametric modeling may be used to find a digital filterthat approximates a prescribed time domain response.

FIG. 3 shows a simulation of an embodiment of a feedback filter in aTomlinson-Harashima precoder scheme using autoregressive moving averagemodeling as compared to a feedback filter of a standardTomlinson-Harashima precoder. The standard Tomlinson-Harashima precoderhas a FIR feedback filter and the ARMA implemented feedback filter is anARMA(6, 5) IIR filter. Data points 310-314 are for the FIR filter andcurve 320 for the ARMA(6, 5) IIR filter. Curve 320 and data points310-314 demonstrate that the impulse response for the IIR fitter isapproximately the same as for the FIR filter.

FIG. 4 shows a simulation of an embodiment of a feedforward filter in aTomlinson-Harashima precoder scheme using autoregressive moving averagemodeling as compared to a feedforward filter of a standardTomlinson-Harashima precoder. The standard Tomlinson-Harashima precoderhas a feedforward FIR filter and the ARMA implemented feedforward filteris an ARMA(3, 3) IIR filter. Data point 410 is for the FIR filter andcurve 420 for the ARMA(3, 3) IIR filter. Curve 420 and data point 410demonstrate that application of an ARMA(3,3) IIR approximation for thetarget feedforward filter provides a result approximately the same asfor the FIR filter.

FIG. 5 shows a simulation of an embodiment of a Tomlinson-Harashimaprecoder scheme using autoregressive moving average modeling withrespect to a bit error rate (BER) for a 100 m category 7 cable. Theperformance of resulting precoding scheme using IIR filters fordifferent number of poles and zeros in ARMA approximations is shown atFIG. 5. Curve 540 having essentially the same performance as curve 510has a feedforward IIR filter with a ARMA 3-pole, 3-zero model plus aARMA 6-pole, 5-zero model for the feedback filter. The lower BER isobtained with curves 520 and 530 having essentially the sameperformance. Curve 520 is for a feedback filter approximated with anARMA 6-pole, 5-zero model. Curve 530 is for a feedforward filterapproximated with an ARMA 3-pole, 3-zero model.

In an embodiment, the number of filter taps may be reduced from 150 fora classical THP feedback filter to 12 for a THP ARMA approximatedfeedback filter. In an embodiment, the number of filter taps may bereduced from 30 for a classical THP feedforward filter to 7 for a THPARMA approximated feedforward filter. In an embodiment, the performanceloss of an ARMA IIR filter design with a feedback filter having 12filter taps and feedforward filter having 7 filter taps may be at most0.3 dB in comparison with a classical FIR preceding scheme. However,such a reduction in the number of filter taps for THP feedback andfeedforward filters may reduce the complexity for implementation of aTomlinson-Harashima precoder complexity in a 10G network. In addition,ARMA approximation of a feedforward filter may be insensitive to itscoefficients quantization. For example, for an ARMA approximation of afeedforward filter, there may be no transmission quality loss if 10 bitsare reserved to represent fractional part of IIR filter taps as comparedto the non-quantized case.

Various embodiments for a Tomlinson-Harashima precoding scheme mayreduce computation and memory load during transmission due to IIRfilters usage. Filters constructed in such a manner may be used in 10Gigabit Ethernet apparatus and systems. Such filters may also beimplemented in other high speed communication-oriented applications.

Network 200 of FIG. 2 may include other apparatus and systems forcommunicating between network nodes 202 and 203. Each node may receiveand transmit information. Network nodes may each include a number ofsystems that may effectively be coupled to a precoder as in FIG. 2 tocommunicate over channel 210. Systems at these nodes may provide one ormore functions at a node. A nodal system may direct operations of othersystems and/or apparatus at the node. Systems at each network node (202,203) may include external connections to each other that are wired orwireless. In an embodiment, nodal systems may be realized as a switch, arouter, a computer, a server, or combination of these elements. Further,nodal systems may couple to each other or other apparatus at a node overa medium that is compatible with Peripheral Component Interconnect (PCI)or with PCI express.

The network nodes (202, 203) each may represent processing systemshaving a physical layer (PHY) entity arranged to operate in accordancewith 10GBase-T as defined by the IEEE 802.3an series of standards, forexample. The 10GBase-T PHY may interface with, for example, a 10G mediaaccess control (MAC) and Gigabit Media Independent Interface (XGMII) inthe IEEE architecture. The 10GBase-T PHY may include part of a networkinterface card (NIC), for example. Nodes (202, 203) may include anyprocessing system and/or communications device suitable for use with a10GBase-T device. For example, node pair (202, 203) may be implementedas a pair of switches, a pair of routers, a pair of servers, a switchand a router, a switch and a server, a server and a router, and soforth. In addition, nodes (202, 203) also may be part of a modularsystem in which 10GBase-T is the high-speed connection for the system.Further, examples for nodes (202, 203) may include high-end servers,supercomputers, clusters, grid computing, workgroup switch uplinks,aggregation uplinks, storage systems, and so forth. The embodiments arenot limited in this context.

Various embodiments or combination of embodiments for apparatus andmethods for constructing a feedback filter in a Tomlinson-Harashimapreceding scheme to match a feedforward filter, where the feedforwardfilter is approximated using autoregressive moving average modeling, maybe realized in hardware implementations, software implementations, andcombinations of hardware and software implementations. ASteiglitz-McBride algorithm may be applied to an autoregressive movingaverage modeling for the feedforward and feedback filters. Variousimplementations may include a machine-readable medium havingcomputer-executable instructions for performing various embodimentssimilar to embodiments discussed herein. The instructions may includeinstructions to approximate a feedforward filter using ARMA modeling.The instructions may include instructions to acquire an ARMAapproximation of a feedforward filter and to construct a feedback filterto match the approximated feedforward filter. The machine-readablemedium is not limited to any one type of medium. The machine-readablemedium used will depend on the application using an embodiment.

FIG. 6 illustrates a block diagram of an embodiment of a system 600having an embodiment of a Tomlinson-Harashima precoder scheme based onan autoregressive moving average modeling. System 600 may include acontroller 610, a memory 620, and a bus 630, where bus 630 provideselectrical connectivity between controller 610 and memory 620 andbetween controller 610 and a communication unit 640. Bus 630 may be aparallel bus. Bus 630 may be a serial bus.

Communication unit 640 may include an embodiment of a feedback filter ina Tomlinson-Harashima precoding scheme to match a feedforward filter,where the feedforward filter and the feedback filter may be approximatedusing autoregressive moving average modeling similar to the schemesdiscussed with respect to FIGS. 1 and 2. Communication unit 640 maycouple to a wired network or a wireless network. Alternatively,communication unit 640 may include a network interface to couple to awired network and to a wireless network. A wired network may include anetwork having wire channels, fiber optic channels, and/or co-axialchannels.

An embodiment may include an additional peripheral device or devices 660coupled to bus 630. Bus 630 may be compatible with PCI or with PCIexpress. In an embodiment, communication unit 640 may include a networkinterface card. In an embodiment, communication unit 640 may include acommunications device suitable for use with a 10Base-T device.Communication unit 640 may include a connection 645 to a wired network.Connection 645 may be configured to connect to a cable 647. Connection645 may be configured to connect to an unshielded twisted pair cable.Connection 645 may be configured to connect to a shielded twisted paircable. In a wireless embodiment, communication unit 640 may be coupledto an antenna 650. In an embodiment, antenna 650 may be a substantiallyomnidirectional antenna. System 600 may include, but is not limited to,information handling devices, wireless systems, telecommunicationsystems, fiber optic systems, electro-optic systems, and computers.

In an embodiment, controller 610 is a processor. Memory 620 may includeany form of machine-readable medium that has machine executableinstructions to acquire an approximation of a feedforward filter in aTomlinson-Harashima precoder scheme, where the feedforward filter isapproximated using autoregressive moving average modeling, and toconstruct a feedback filter to match the approximated feedforwardfilter. In an embodiment, the feedback filter may be approximated usingautoregressive moving average modeling. The machine may include acomputer. Peripheral devices 660 may also include displays, additionalstorage memory, or other control devices that may operate in conjunctionwith controller 610. Alternatively, peripheral devices 660 may includedisplays, additional storage memory, or other control devices that mayoperate in conjunction with controller 610, communication unit 640,and/or memory 620.

In a wireless arrangement in which the transmission medium betweentransmitter and receiver is relatively steady or slowly varying, thechannel characteristics may be modeled or determined. With a givenwireless channel model, an approximation of a feedforward filter in aTomlinson-Harashima precoder scheme using an autoregressive movingaverage modeling may be acquired, and a feedback filter may beconstructed to match the approximated feedforward filter in a mannersimilar to embodiments discussed herein. The feedforward filter may beconstructed using an autoregressive moving average modeling and applyinga Steiglitz-McBride algorithm. Various embodiments for constructingfeedforward filters and their associated feedback filters may beimplemented for a wireless application having a relatively steady orslowly varying transmission medium.

Although specific embodiments have been illustrated and describedherein, it will be appreciated by those of ordinary skill in the artthat any arrangement that is calculated to achieve the same purpose maybe substituted for the specific embodiments shown. This application isintended to cover any adaptations or variations of embodiments of thepresent invention. It is to be understood that the above description isintended to be illustrative, and not restrictive, and that thephraseology or terminology employed herein is for the purpose ofdescription and not of limitation. Combinations of the above embodimentsand other embodiments will be apparent to those of skill in the art uponreviewing the above description. The scope of the present inventionincludes any other applications in which embodiment of the abovestructures and fabrication methods are used. The scope of theembodiments of the present invention should be determined with referenceto the appended claims, along with the fill scope of equivalents towhich such claims are entitled.

1. A method comprising: acquiring an approximation of a feedforwardfilter in a Tomlinson-Harashima precoder scheme, the feedforward filterbeing approximated using autoregressive moving average modeling; andconstructing a feedback filter to match the approximated feedforwardfilter, wherein constructing the feedback filter includes generating atarget feedback filter from the approximation of the feedforward filterand conducting autoregressive moving average modeling of the targetfeedback filter to construct the feedback filter.
 2. The method of claim1, wherein acquiring the approximation of the feedforward filterincludes approximating a set of feedforward filters using autoregressivemoving average modeling, the set corresponding to communication channelsof varying characteristics.
 3. The method of claim 2, wherein thevarying characteristics include different channel lengths.
 4. The methodof claim 1, wherein constructing the feedback filter includesconstructing an infinite impulse response filter to match a feedforwardinfinite impulse response filter approximated using the autoregressivemoving average modeling.
 5. The method of claim 1, wherein constructingthe feedback filter includes constructing a Tomlinson-Harashima precoderfeedback filter having less than 15 filter taps.
 6. The method of claim1, wherein acquiring the approximation of the feedforward filterincludes acquiring an approximation of a feedforward filter having lessthan 10 filter taps.
 7. A non-transitory machine-readable storage mediumhaving instructions stored thereon, which when performed by a machine,cause the machine to: acquire an approximation of a feedforward filterin a Tomlinson-Harashima precoder scheme, the feedforward filterapproximated using autoregressive moving average modeling; and constructa feedback filter to match the approximated feedforward filter, whereinconstructing the feedback filter includes generating a target feedbackfilter from the approximation of the feedforward filter and conductingautoregressive moving average modeling of the target feedback filter toconstruct the feedback filter.
 8. The non-transitory machine-readablestorage medium of claim 7, wherein to acquire the approximation of thefeedforward filter includes approximating a set of feedforward filtersusing autoregressive moving average modeling, the set corresponding tocommunication channels of varying characteristics.
 9. The non-transitorymachine-readable storage medium of claim 7, wherein instructions thatcause the machine to construct the feedforward filter includeinstructions that cause the machine to construct an infinite impulseresponse filter to match an infinite impulse response filter feedbackfilter.
 10. The non-transitory machine-readable storage medium of claim7, wherein instructions that cause the machine to construct the feedbackfilter include instructions that cause the machine to construct aTomlinson-Harashima precoder feedback filter having less than 20 filtertaps.
 11. An apparatus comprising: a feedback filter in aTomlinson-Harashima precoder, the Tomlinson-Harashima precoder capableof coupling to a physical communication channel, the feedback filter tomatch a feedforward filter, the feedforward filter having filter taps,the filter taps being autoregressive moving average modelingapproximated filter taps; and a processor and a memory operativelycoupled to the processor, the processor and the memory arranged toacquire an approximation of the feedforward filter approximated usingautoregressive moving average modeling and to construct the feedbackfilter such that the construction includes generating a target feedbackfilter from the approximated feedforward filter and conductingautoregressive moving average modeling of the target feedback filter toconstruct the feedback filter.
 12. The apparatus of claim 11, whereinthe feedback filter includes an infinite impulse response filter tomatch the feedforward filter arranged as infinite impulse responsefilter.
 13. The apparatus of claim 11, wherein the feedback filterincludes a feedback filter having less than 20 filter taps.
 14. Theapparatus of claim 11, wherein the feedback filter includes a feedbackfilter to match a Tomlinson-Harashima precoder feedforward filter havingless that 15 filter taps.
 15. The apparatus of claim 11, wherein thefeedback filter includes a feedback filter matched to a feedforwardfilter to provide equalization in 10 gigabit Ethernet operation.
 16. Asystem comprising: a controller; a parallel bus; and a feedback filterin a Tomlinson-Harashima precoder scheme, the feedback filtercommunicatively coupled to the controller through the parallel bus, thefeedback filter to match a feedforward filter, the feedforward filterhaving filter taps, the filter taps being autoregressive moving averagemodeling approximated filter taps; and a memory operatively coupled tothe controller, the controller and the memory arranged to acquire anapproximation of the feedforward filter approximated usingautoregressive moving average modeling and to construct the feedbackfilter such that the construction includes generating a target feedbackfilter from the approximated feedforward filter and conductingautoregressive moving average modeling of the target feedback filter toconstruct the feedback filter.
 17. The system of claim 16, wherein thefeedback filter includes an infinite impulse response filter to matchthe feedforward filter arranged as infinite impulse response filter. 18.The system of claim 16, wherein the feedback filter includes thefeedback filter being compatible with a 10 Gigabit Ethernet.
 19. Thesystem of claim 16, wherein the feedback filter includes the feedbackfilter having less than 20 filter taps.
 20. The system of claim 16,wherein the system includes the feedforward filter in theTomlinson-Harashima precoder scheme to provide bi-directionalcommunication, the feedforward filter having autoregressive movingaverage modeling approximated filter taps.